1

Cure Kinetics of Ring-Opening MetathesisPolymerization of Dicyclopentadiene*

M. R. Kessler1, S. R. White2

1Department of Theoretical and Applied Mechanics2Department of Aeronautical and Astronautical Engineering

University of Illinois at Urbana-ChampaignUrbana-Champaign, IL, USA

Abstract: The cure kinetics of polydicyclopentadiene (pDCPD) prepared by ring-opening metathesis polymerization with three different concentrations of Grubbs’catalyst was examined using differential scanning calorimetry (DSC). Theexperimental data were used to test several different phenomenological kineticmodels. The data are best modeled with a “model-free” isoconversional method. Thisanalysis reveals that the activation energy increases significantly for degree of curegreater than 60%. Catalyst concentration is shown to have a large effect on the curekinetics.Keywords: differential scanning calorimetry (DSC), kinetics (polym.), activationenergy, ROMP, dicyclopentadiene.

INTRODUCTION

Polydicyclopentadiene (pDCPD) is generally a highly crosslinked polymer ofhigh toughness formed by a ring-opening metathesis polymerization (ROMP) of itsmonomer precursor. The polymerization is highly exothermic due to the relief of ringstrain energy and can be initiated by transition-metal alkylidene complexes. A recentlydeveloped ruthenium-based catalyst (Grubbs’ catalyst) shows high metathesis activitywhile being tolerant of a wide range of functional groups as well as oxygen and water [1].

The polymerization of DCPD with Grubbs’ catalyst in reaction injection molding(RIM) and resin transfer molding (RTM) applications results in a polymer with excellentmechanical properties and little chemical shrinkage [2]. Recently, White et al. [3]reported on a materials system that incorporates dicyclopentadiene (DCPD) and Grubbs’catalyst into an epoxy matrix to autonomically repair the material when it is damaged.Similarly, Kessler and White [4] used DCPD to repair delamination damage in laminatecomposites in which the Grubbs’ catalyst was embedded in the matrix of the compositematerial.

In self-healing applications the polymerization kinetics determine the extent towhich polymerization can occur for a given time and at a particular temperature and thus,the healing efficiency. In RIM and RTM applications the kinetics influence thethermochemical history of the part, ultimately dictating the processing time and finalphysical properties. Modeling the cure kinetics of DCPD and Grubbs’ catalyst has utility * Submitted for publication to Journal of Polymer Science Part A: Polymer Chemistry

2

not only in optimizing self-healing materials, but also the processing of RIM/RTMfabricated pDCPD.

In phenomenological modeling of the cure kinetics of thermosetting polymers aninternal state variable is defined to which all other properties are related. This statevariable is the degree of cure (α) and ranges from zero (uncured) to one (fully cured).Thermal analysis by differential scanning calorimetry (DSC) is the most commonly usedexperimental technique to determine the cure kinetics of thermosets [5]. For DSCmeasurements the degree of cure is defined as

α ( )( )

tH t

HR

= (1)

where H(t) is the enthalpy of reaction up to time t, and HR is the total enthalpy ofreaction. The DSC provides a continuous history of the heat evolved duringpolymerization which can then be integrated to yield H(t) and through Eq. (1) the degreeof cure history is obtained.

Traditionally, the determination of kinetic parameters from DSC measurements isaccomplished using isothermal data [5]. Isothermal measurements do have the advantageof a complete separation between the variables of time and temperature. However,significant advancement of the cure state can take place before the DSC can reach andstabilize at the desired temperature, and at low temperatures the reaction may not proceedto completion. Alternatively, dynamic data allow for a better capture of the kinetics atboth the start and end of a reaction and complex reaction mechanisms can be more easilyinterpreted by comparing measurements at different heating rates.

In this study a phenomenological cure kinetics model is developed from dynamicDSC data of DCPD cured with Grubbs’ catalyst over a range of catalyst concentrations.The experimental data were used to test several different phenomenological kineticmodels over a range of heating rates from 2-15°C⋅min-1.

MATERIALS AND METHODS

Materials. DCPD monomer stabilized with 100 – 200 ppm p-tert-butylcatecholwas purchased from Acros Organics (Geel, Belgium). As supplied, the monomer ispredominantly endo isomer. The monomer was purified by low vacuum distillation toremove any trace impurities. Bis(tricyclohexylphosphine)benzylidine ruthenium (IV)dichloride (Grubbs’ catalyst) was purchased from Strem Chemicals (Newburyport, MA)in the form of a fine purple powder. The catalyst was stored and prepared in a glove boxwith N2 purge to minimize decomposition over time.

The mixing of DCPD with Grubbs’ catalyst initiates the ROMP reaction shown inFigure 1. This ROMP reaction can be extremely rapid at room temperature, dependingon the catalyst concentration and sample size. The polymerization of DCPD wasaccomplished using three different catalyst to monomer ratios as shown in Table 1.

Technique. Vials each containing 20 mg, 30 mg, or 40 mg of catalyst and asmall Teflon®-coated magnetic stir bar were placed in a water bath at 15°C. To eachwas added 15 ml of distilled DCPD, also cooled to 15°C, and the solutions were mixedvigorously using the magnetic stirrer for about 30 seconds, by which time the catalystpowder had dissolved and a homogeneous solution was achieved for the threeconcentrations listed in Table 1. The vials were then immediately placed in liquid

3

nitrogen to flash-freeze the solution and stored in a –80°C freezer. A typical DSC samplewas prepared by removing a small amount of the frozen solution and placing it in analuminum DSC pan, weighing the sample, and loading it in the DSC chamber at astandby temperature of –5°C. The average and standard deviation in sample size was 9.8mg and 1.9 mg, respectively.

DSC measurements were performed using a Mettler Toledo DSC821e connectedto a computer equipped with STARe v 6.0 evaluation software to manipulate and transferdata. The DSC cell was swept by a constant flow of nitrogen at 80 ml⋅min-1. The DSCwas first calibrated in duplicate for temperature and heat flow accuracy using indium,water, octane, and zinc standards. Tests were performed on the DCPD/catalyst system indynamic mode at various heating rates over the temperature range from –50 to 250°C.Data obtained from heating rates of 2, 5, 7, 10, and 15°C⋅min-1 were converted to ASCIIformat and kinetic analysis was performed using Netzsch Thermokinetics program (v.2001.2), Mathematica (v. 4.1.1), and standard statistical and plotting programs.

CURE KINETIC MODELING

Model-Fitting Method. In kinetic analysis it is generally assumed that the rate ofreaction can be described by two separable functions K(T) and f(α) such that

ddα αt

K T f= ⋅( ) ( ) (2)

where dα/dt is the rate of reaction, K(T) is the temperature dependent rate constant, andf(α) corresponds to the reaction model. The temperature dependence of the reaction rateis commonly described by the Arrhenius equation

K T AE

RT( ) exp= ⋅ −

(3)

where R is the universal gas constant, E is the activation energy and A is the pre-exponential factor.

For experiments in which samples are heated at a constant rate, the explicit timedependence in Eq. (2) can be eliminated so that

ddα

βα

T

A E

RTf= ⋅ −

⋅exp ( ) (4)

where β = dT/dt is the heating rate.A multivariate version of the Borchardt and Daniels method [6] is frequently used

in the evaluation of dynamic DSC data. In this method the kinetic parameters (A, E) areobtained by a linearizing transformation of Eq. (4) so that

ln( )

lnd dα

α βT

f

A E

RT=

− (5)

This linear equation, which has the form y = a0+a1x with x = 1/T, can be used todetermine the optimal fit of the kinetic parameters by multiple linear regression.

“Model-Free” Isoconversional Method. The “model-free” isoconversionalmethod assumes that both the activation energy and the pre-exponential factor arefunctions of the degree of cure. The activation energy is determined by Friedman’smethod [7] from the logarithmic form of the rate equation for each heating rate:

4

ln / ln,,

β α αα αα

αi i

i

d dT A fE

RT( )[ ] = ( )( ) − (6)

where the subscript α is the value at a particular degree of cure and i refers to data from agiven heating rate experiment. The activation energy at each degree of cure is calculatedusing linear regression from a plot of ln[βi(dα/dT)α,i] versus 1/Tα,i (Friedman plot) acrossall of the heating rates tested. Similarly, the product of cure dependent pre-exponentialfactor and the reaction model can be obtained from the y-intercept of the Friedman plot.These parameters can alternately be calculated by an integral isoconversional methoddescribed by Flynn and Wall [8] and Ozawa [9].

The isoconversional approach can be used to evaluate both simple and complexchemical reactions. For evaluation of data using this method no kinetic rate expression isassumed a priori.

EXPERIMENTAL RESULTS

A typical DSC scan and the corresponding degree of cure is shown in Figure 2.When the scan begins at –50°C the sample is a frozen solid. Near -5°C a broadendothermic peak initiates and extends from –5 to 15°C. This endothermic peakcorresponds to the melting of the DCPD. Superimposed on this melting transition is asharp endothermic peak at 0°C corresponding to the presence of water in the sample,presumably condensation resulting from the flash freezing of the sample in liquidnitrogen immediately after mixing. Analyzing the size of the peak and assuming 2400J⋅g-1 for ∆H of water, the total content of water was determined to be less than 0.005% forall samples analyzed. Later tests on samples that were not flash frozen showed noendothermic melting peak at 0°C, but otherwise were identical to those that were flashfrozen. To correct for these melting transitions in the evaluation of the degree of cure, abest fit spline connecting the pre- and post-melt regions was constructed (the dashed linein Figure 2) to effectively eliminate the melting phenomenon from the heat flow curves.As a justification, less than 0.5% of cure advancement occurs before the end of themelting region and as such, has little influence on the overall cure kinetics.

The baseline used to determine the total heat released and the degree of cure isalso shown in Figure 2. Subsequent dynamic plots are presented having corrected for themelting transition and subtracting the baseline from the heat flow data. The degree ofcure is then calculated from the corrected plots.

Figure 3 shows the DSC scans for all of the experimental runs used to create thekinetic models reported herein. As the catalyst concentration increases, the exothermicpeak shifts to lower temperatures for a given heating rate. For the lowest concentrationtested (Figure 3a), at 2°C⋅min-1 there was excessive weight loss (over 9%) fromevaporation of DCPD, so this case was discarded and only four heating rates were usedfor model fitting the low concentration data. Table 2 shows the final and initial samplesizes and the total enthalpy of reaction measured for each sample. The average totalenthalpy of reaction for all experiments is 461±14.1 J⋅g-1 and there was no noticeabledependence on heating rate.

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MODEL PERFORMANCE

Five different reaction models (Table 3) were used to fit the experimental data byan appropriate multivariable least-squares regression fitting method. The first- andsecond-order models are the simplest and only require two fitting parameters (E and A).The nth-order reaction model is more general and allows for better fits to the data byletting the order of the reaction be determined empirically. The most complex modelsinvestigated require four fitting parameters and including both the nth-order autocatalysismodel and the expanded Prout–Tompkins (autocatalytic) model [10,11]. Ng and Manas-Zloczower [11] used the Prout–Tompkins model for a DCPD-based reaction injectionmolding (RIM) system and found good agreement with experimental results using anadiabatic temperature rise method where the rate of temperature change is related to therate of reaction through an energy balance for the adiabatic case.

The results of the multiple linear regression analysis for all the models are listedin Table 4. The experimental fits that were obtained are also shown in Figure 4 for themedium catalyst concentration mixture. Based on the LSQ correlation coefficient (seeAppendix) the nth-order autocatalytic model gives the best fit to the data over the heatingrates investigated. An F-test statistical analysis (see Appendix) confirms this and theresults of the analysis are given in Table 5.

In order to determine a model-free estimation for the activation energy, aFriedman plot is first created by using the logarithmic form of the rate equation (Eq. (6))for all of the heating rates. A Friedman plot for the medium catalyst concentration case isshown in Figure 5. The activation energy and the product of A* f(α) at each degree ofcure is calculated by linear regression at a specific value of α. The straight lines inFigure 5 correspond to these linear fits for α values ranging from 0.02 to 0.98.

The complex dependence of the activation energy on the degree of cure can beseen in Figure 6 for all three catalyst concentrations. It is immediately apparent that theactivation energy increases significantly for all three concentrations after the degree ofcure reaches about 0.6 and especially near the end of cure. The assumption of constantactivation energy (as is the case for all of the reaction models listed in Table 4) isreasonable up to this critical degree of cure, but too restrictive for the entire cure range.One interpretation of this behavior is an apparent decrease of molecular mobility as thedegree of cure increases above 0.6 and the polymer gels. It is also apparent that theactivation energy for all three catalyst concentrations are quite comparable. Finally, theplot of the product of ln[A* f(α)] appears to vary similarly to the activation energy withdegree of cure. This correspondence is due to the isokinetic relationship [7,12] or thekinetic compensation effect [13] which suggests that the value of ln Aα varies linearlywith Eα . Such a relationship has been observed in the curing and decomposition ofnumerous other polymer systems [14-17].

A fifteenth-order polynomial was used to fit the E and ln[A* f(α)] data fromFigure 6 and together with Eq. (4), predictions for the cure rate at various heating rateswere obtained. Figure 7 shows these model-free predictions compared with theexperimental data for the medium catalyst concentration case. Excellent agreement isapparent over all of the heating rates investigated.

Model predictions for isothermal curing at 30°C for the medium catalystconcentration case together with the experimental data for a 15 hr isothermal cure are

6

plotted in Figure 8. During the first hour of curing the model-free prediction fits theexperimental data extremely well. The major differences between the various kineticmodels are readily apparent at longer times. Particularly, the model-free predictionsuggests that the ultimate degree of cure is significantly lower than any of the reactionmodels because of the increase in activation energy for α > 0.6 (see Figure 6). While theisothermal model-free fit deviates from the experimental values for degrees of cure above0.5 (Figure 8), it does a much better job of predicting the isothermal cure kinetics thanany of the model fitting approaches.

Subsequent to the 15 hr isothermal cure at 30°C, these samples were then scannedat 15°C⋅min-1 from –50 to 220°C in the DSC. These scans for all three catalystconcentrations are shown in Figure 9. Also included in Figure 9 is a dynamic scan at15°C⋅min-1 of a fully cured (low catalyst concentration) sample, which yields a glasstransition temperature of 139°C. The glass transition temperatures after isothermalcuring for the low, medium, and high catalyst concentration samples are 28.7, 43.7, 48.7,respectively. It is apparent from the results that further polymerization does not occuruntil after the sample reaches the glass transition temperature. One reason for thedeviation between the model-free prediction and the isothermal data for degrees of cureabove 0.5 is the difference in curing conditions. Specifically, the dynamic data uponwhich the model-free fit is based was obtained by curing above the glass transitiontemperature whereas the isothermal data eventually reaches conditions in which curingoccurs below the glass transition. To more accurately model the isothermal case atdegrees of cure above 0.5 a model that includes the influence of the cure dependent glasstransition temperature should be employed.

Another feature of the medium and high concentration scans in Figure 9 is thepresence of an endothermic peak in the Tg region before the larger exothermic curingpeak. Similar endothermic peaks attributed to enthalpic relaxation or physical aging areoften seen in glassy polymers as a result of slow cooling through the glass transitionregion or annealing below Tg [18]. The annealing time and temperature has a large affecton the position and magnitude of these annealing peaks. For the medium and highcatalyst concentration cases, the end of the annealing peak is superimposed with thebeginning of the exothermic curing peak. Thus, the measured glass transitiontemperature for these cases slightly overestimates the true Tg. The presence of thesesuperimposed annealing peaks also complicates the measurement of the residual heat ofreaction for these cases.

The isothermal model-free predictions for all three catalyst concentrations at 30°Cis shown in Figure 10. The predictions show a significant difference between the low andthe high concentrations for the time necessary to reach a given degree of cure. Forexample, the degree of cure for the high catalyst concentration is nearly double that of thelow catalyst concentration case after 60 minutes at 30°C.

CONCLUSIONS

In this work, several reaction models were used to analyze dynamic DSC data forthe cure of DCPD with three different concentrations of Grubbs’ catalyst. It was shownthat the catalyst concentration has a large effect on the cure kinetics. Of the standardreaction models, the nth-order autocatalytic model performed the best. However, the

7

model-free isoconversional method provided the best fit of the data over the range ofhealing rates investigated. From the isoconversional method, the activation energy wasshown to increase significantly for α > 0.6. As a result, the model-free method predicts alower degree of cure for long periods of time compared with any of the standard reactionmodels. This behavior was qualitatively verified by isothermal cure experiments at 30°C.

APPENDIX: STATISTICAL EVALUATION

The correlation coefficient (r) is defined as

rLSQ

Y Y Ns k s kkk

sS

= −− ∑∑∑

1 2 2( ( ) / ), ,

(A1)

LSQ Y Yj k j k

k

N

j

S s

= −==

∑∑ ( ),

^

,

11

2 (A2)

where Yj,k is the measured value, Yj k

^

, is the regress value, S is the number of scans, andNS is the number of measured values in a particular scan.

The F-test compares the residual variances of the individual models against oneanother. It is used to assess whether there is a statistically significant difference betweenthe models with respect to the quality of fit to the experimental data. The model with thelowest correlation coefficient is typically taken as the reference model. The F-test valueis then defined as

F f f

Y Y f

Y Y f

j k j k

k

N

j

S

j k j k

k

N

j

S

s

sexp

,

^

,

,

^

,

( , )

( ( )) /

( ( )) /1 2

11

21

11

22

=−

−

==

==

∑∑

∑∑

model

model

1

2

(A3)

where f1 is the degree of freedom of model1 and f2 is the degree of freedom of model2 (thereference model) [19]. Fexp is then compared with the critical value of the F distribution,F f fcrit ( , )1 2 , for a given confidence level. An Fexp< Fcrit indicates no statistical differencewhile Fexp>Fcrit indicates model1 is significantly better suited to characterize theexperimental data.

ACKNOWLEDGMENTS

The research described in this paper was supported by a grant from the Air Force Officeof Scientific Research (Grant No. F49620-00-1-0094) and by a graduate fellowship fromthe Beckman Institute for Advanced Science and Technology at the University of Illinoisat Urbana-Champaign. Thanks are extended to Josh Orlicki for assistance and training onthe DSC and thoughtful discussion. We are also grateful to Jeff Moore for his insightsand review and to Nancy Sottos, Paul Braun, Eric Brown, and Suresh Sriram for theirtechnical support.

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REFERENCES

[1] Schwab, P.; Grubbs, R. H.; Ziller, J. W. J Am Chem Soc 1996, 118, 100-110[2] Macosko, C. W. RIM, Fundamentals of Reaction Injection Molding 1989, New York.[3] White, S. R.; Sottos, N. R.; Geubelle, P. H.; Moore, J. S.; Kessler, M. R.; Sriram, S. R.; Brown, E. N.;

Viswanathan, S. Nature 2001, 409, 794-797.[4] Kessler, M. R.; White, S. R. Compos Part A: Appl Sci Manuf 2001, 32(5), 683-699.[5] Halley, P. J.; Mackay, M. E. Polym Eng Sci 1996, 36(5), 593-608.[6] Borchardt, H. J.; Daniels, F. J Am Chem Soc 1957, 79, 41-46.[7] Friedman, H. L. J Polym Sci Part C: Poly Symp 1963, 6, 183.[8] Flynn, J. H.; Wall, L. A. J Polym Sci Part B: Polym Lett 1966, 4, 323-328.[9] Ozawa, T. Bull Chem Soc Japan 1965, 38(38), 1881.[10] Shin, D. D.; Hahn, H. T. Compos Part A: Appl Sci Manuf 2000, 31, 991-999[11] Ng, H; Manas-Zloczower, I. Polym Eng Sci 1994, 34(11), 921-928.[12] Vyazovkin, S. Int J Chem Kinet 1996, 28, 95-101.[13] Pielichowski, K.; Czub, P.; Pielichowski, J. Polymer 2000, 4381-4388.[14] Cooney, J. D.; Day, M.; Wiles, D. M. J Appl Polym Sci 1984, 29, 911-923.[15]MacCallum, J. R.; Munro, M. V. Thermochim Acta 1992, 203, 457.[16] Montserrat, S.; Flaque, C.; Pages, P.; Malek, J. J Appl Polym Sci 1995, 56, 1413-1421.[17] Montserrat, S.; Andreu, G.; Cortes, P.; Calventus, Y.; Colomer, P.; Hutchinson, J. M.; Malek, J. J Appl

Polym Sci 1996, 61, 1663-1974.[18] McKenna, G. In Comprehensive Polymer Science, Vol. 2, Polymer Properties; Booth, C.; Price, C.,

Ed.; Oxford, 1989, pp 311-362.[19] Netzsch Thermokinetics (v. 2001.2), Statistical Evaluation of Results, program help, 2001.

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Table 1 Three concentrations of catalyst analyzed.Designation g catalyst/ ml DCPD* Catalyst molecules : DCPD molecules**

Low 1.33E-3 1:5000Medium 2.00E-3 1:3750High 2.67E-3 1:2500*Density of DCPD is 1.0710 g/cm3

** MW of DCPD & catalyst is 132.2 & 822.96, respectively

Table 2 Sample size and measured total enthalpy of reaction.Sample sizeHeating rate

initial final

Total enthalpyof reaction

Concentration

(°C/min) (mg) (mg) (J/g)15 9.3 8.9 456.710 10.3 9.8 459.97 8.3 8.1 453.55 7.8 7.4 443.5

Low

15 9.1 8.9 463.810 6.3 6.1 457.37 7.2 7.1 461.65 11.6 11.3 478.82 12.6 12.3 436.8

Medium

15 11.2 11.2 472.610 10.8 10.7 485.37 11.9 11.9 474.15 11.1 11.1 467.5

High

2 10.3 10.2 442.6

Table 3 Reaction models evaluated.Reaction model Model

designationf(α) Parameters

first-order F1 (1-α) A, Esecond-order F2 (1-α)2 A, E

nth-order Fn (1-α)n A, E, nnth-order with autocatalysis Cn (1-α)n(1+Kcatα) A, E, n, Kcat

Prout–Tompkins equation (autocatalytic) PT (1-α)nαm A, E, n, m

10

Table 4 Results of multiple linear regression analysis.Catalyst

concentrationModel

designationlog[A] (s-1)

E(kJ/mol)

n Kcat m Correlationcoefficient

Low F1 4.961 51.31 - - - 0.9822F2 8.563 75.69 - - - 0.9788Fn 6.199 59.65 1.328 - - 0.9864Cn 4.409 48.76 1.616 0.436 - 0.9917PT 5.653 55.50 1.335 - 0.093 0.9865

Medium F1 4.698 46.55 - - - 0.9815F2 8.083 67.97 - - - 0.9921Fn 7.019 61.21 1.671 - - 0.9934Cn 5.281 51.10 1.927 0.365 - 0.9965PT 5.899 53.27 1.668 - 0.168 0.9942

High F1 5.240 48.59 - - - 0.9757F2 8.834 70.86 - - - 0.9938Fn 8.657 69.76 1.948 - - 0.9938Cn 6.649 58.16 2.192 0.370 - 0.9966PT 7.230 60.02 1.923 - 0.176 0.9947

Table 5 F-test statistical analysis of the model fits in Table 4.Fexp

*Catalystconcentration Cn PT Fn F2 F1

Low 1.00 1.69 1.71 2.67 2.20

Medium 1.00 1.72 1.97 2.38 5.41

High 1.00 1.57 1.79 1.80 6.97*Fcrit=1.1 for a 95% confidence level

11

RuCl

ClPCy3

PCy3

Ph

H

DCPDMonomer Grubbs' Catalyst

Crosslinked PolymerNetwork

Figure 1. Ring-opening metathesis polymerization (ROMP) of dicyclopentadiene(DCPD) with Grubbs' catalyst.

-0.2

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0.8

1

-50 0 50 100 150 200

Hea

t flo

w r

ate

(W/g

)

Deg

ree

of c

ure,

α

Temperature ( οC)

Baseline

Melting of DCPDsmoothed out

Cubicspline fit

Watermelt

DCPD melt

Figure 2. Typical DSC scan (at 5°C/min) and corresponding degree of cure history(Note: 1:3750 catalyst concentration)

12

0

0.5

1

1.5

2

2.5

0 50 100 150 200

15.0 K/min10.0 K/min7.0 K/min5.0 K/min

Hea

t flo

w r

ate

(W/g

)

Temperature (oC)

increasingheating rate

exo

0

0.5

1

1.5

2

2.5

0 50 100 150 200

15.0 K/min10.0 K/min7.0 K/min5.0 K/min2.0 K/min

Hea

t flo

w r

ate

(W/g

)

Temperature (oC)

exo

increasingheating rate

0

0.5

1

1.5

2

2.5

0 50 100 150 200

15.0 K/min10.0 K/min7.0 K/min5.0 K/min2.0 K/min

Hea

t flo

w r

ate

(W/g

)

Temperature (oC)

increasingheating rate

exo

a) b)

c)

Figure 3. DSC curves for (a) low concentration, (b) medium concentration, and (c) highconcentration, DCPD and Grubbs' catalyst samples.

13

0

1

2

3

4

5

0 50 100 150 200

15 K/min10 K/min7 K/min5 K/min2 K/min

Cur

e ra

te, d

α /dt

*10

3 (s-1

)

Temperature (oC)

Fn

0

1

2

3

4

5

0 50 100 150 200

15 K/min10 K/min7 K/min5 K/min2 K/min

Cur

e ra

te, d

α /dt

*10

3 (

s-1)

Temperature (oC)

Cn

0

1

2

3

4

5

0 50 100 150 200

15 K/min10 K/min7 K/min5 K/min2 K/min

Cur

e ra

te, d

α /dt

*10

3 (

s-1)

Temperature (oC)

PT

0

1

2

3

4

5

0 50 100 150 200

15 K/min10 K/min7 K/min5 K/min2 K/min

Cur

e ra

te, d

α /dt

*10

3 (

s-1)

Temperature (oC)

F2

0

1

2

3

4

5

0 50 100 150 200

15 K/min10 K/min7 K/min5 K/min2 K/min

Cur

e ra

te, d

α /dt

*10

3 (s-1

)

Temperature (oC)

F1

a) b)

c) d)

e)

Figure 4. Model fits of DSC data for the medium catalyst concentration. (a) 1st order(F1), (b) 2nd order (F2), (c) nth order (Fn), (d) expanded Prout-Tompkins (PT), (e) nth

order with autocatalysis (Cn).

14

-5

-4.5

-4

-3.5

-3

-2.5

-2

2.4 2.6 2.8 3 3.2 3.4

log

(dα

/dt)

1000 K/T

0.95

0.90

0.80

0.700.60 0.50

0.020.05

0.040.03

0.020.01

α=0.98

Figure 5. Friedman plot for medium catalyst concentration case.

50

100

150

200

250

300

350

400

10

1000

105

107

109

1011

1013

1015

1017

1019

0 0.2 0.4 0.6 0.8 1

E LowE MediumE High

A*f(α) LowA*f(α) MediumA*f(α) High

Act

ivat

ion

Ene

rgy,

E (

kJ/m

ole)

A*f

( α)

(s-1)

Degree of Cure, αFigure 6. Model-free results for the activation energy and the product A* f(α) vs. degree

of cure for all three catalyst concentration cases.

15

0

1

2

3

4

5

0 50 100 150 200

15 K/min10 K/min7 K/min5 K/min2 K/min

Cur

e ra

te, d

α /dt

*103 (

s-1)

Temperature (oC)

Figure 7. Model-free prediction and experimental results for medium catalystconcentration case.

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800

experimental dataF1F2FnCnPTmodel free fit

Deg

ree

of c

ure,

α

Time (min)

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60

Deg

ree

of c

ure,

α

Time (min)

Figure 8. Model predictions for isothermal curing at 30°C for the medium catalystconcentration case overlaid with a 900 min isothermal cure experiment.

16

20 25 30 35 40 45 50 55 60

Hea

t flo

w r

ate

Temperature ( οC)

Low

Medium

High

Fully curedT

g=28.7

Tg=43.7

Tg=48.7

0.25

W/g

0 50 100 150 200

Hea

t flo

w r

ate

Temperature ( οC)

LowMedium

High

Fullycured

0.5

W/g

Tg=139

Figure 9. Dynamic scans (15°C/min) of fully cured control sample and samples just afterthe 30°C, 900 min isothermal runs for low, medium, and high concentrations.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60

high mediumlow

Deg

ree

of C

ure,

α

Time (min)

catalyst concentration

highmediumlow

Figure 10. Predictions for isothermal curing at 30°C based on model-freeisoconversional method for low, medium, and high catalyst concentrations.